Scenario

[(3 3) (2 2)]

Description

Local facet in [(3 3) (2 2)], solved by SymPol.

Cross references

#3

Bell expression and bounds

$$ \left (\begin{array}{rr:rr} \tooltip{- \frac{1}{2}}{P(11|11)} & \tooltip{\frac{1}{2}}{P(21|11)} & \tooltip{- \frac{1}{2}}{P(31|11)} & \tooltip{- \frac{1}{2}}{P(11|21)} & \tooltip{- \frac{1}{2}}{P(21|21)} & \tooltip{\frac{1}{2}}{P(31|21)} \\ \tooltip{\frac{1}{2}}{P(12|11)} & \tooltip{- \frac{1}{2}}{P(22|11)} & \tooltip{\frac{1}{2}}{P(32|11)} & \tooltip{\frac{1}{2}}{P(12|21)} & \tooltip{\frac{1}{2}}{P(22|21)} & \tooltip{- \frac{1}{2}}{P(32|21)} \\ \tooltip{\frac{1}{3}}{P(11|12)} & \tooltip{- \frac{2}{3}}{P(21|12)} & \tooltip{\frac{1}{3}}{P(31|12)} & \tooltip{- \frac{1}{3}}{P(11|22)} & \tooltip{- \frac{1}{3}}{P(21|22)} & \tooltip{\frac{2}{3}}{P(31|22)} \\ \hdashline \tooltip{- \frac{1}{3}}{P(12|12)} & \tooltip{\frac{2}{3}}{P(22|12)} & \tooltip{- \frac{1}{3}}{P(32|12)} & \tooltip{\frac{1}{3}}{P(12|22)} & \tooltip{\frac{1}{3}}{P(22|22)} & \tooltip{- \frac{2}{3}}{P(32|22)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{r|r:r} \tooltip{-1}{P_(|)} & \tooltip{0}{P_A(1|1)} & \tooltip{0}{P_A(2|1)} & \tooltip{2}{P_A(1|2)} & \tooltip{2}{P_A(2|2)} \\ \hline \tooltip{0}{P_B(1|1)} & \tooltip{0}{P_AB(1,1|1,1)} & \tooltip{2}{P_AB(2,1|1,1)} & \tooltip{-2}{P_AB(1,1|2,1)} & \tooltip{-2}{P_AB(2,1|2,1)} \\ \tooltip{2}{P_B(1|2)} & \tooltip{0}{P_AB(1,1|1,2)} & \tooltip{-2}{P_AB(2,1|1,2)} & \tooltip{-2}{P_AB(1,1|2,2)} & \tooltip{-2}{P_AB(2,1|2,2)}\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } \frac{1}{2} \text{ } P(11|11) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(21|11) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(31|11) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(11|21) \\ \text{-} \text{ } \frac{1}{2} \text{ } P(21|21) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(31|21) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(12|11) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(22|11) \\ \frac{1}{2} \text{ } P(32|11) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(12|21) \text{ } \text{+} \text{ } \frac{1}{2} \text{ } P(22|21) \text{ } \text{-} \text{ } \frac{1}{2} \text{ } P(32|21) \\ \frac{1}{3} \text{ } P(11|12) \text{ } \text{-} \text{ } \frac{2}{3} \text{ } P(21|12) \text{ } \text{+} \text{ } \frac{1}{3} \text{ } P(31|12) \text{ } \text{-} \text{ } \frac{1}{3} \text{ } P(11|22) \\ \text{-} \text{ } \frac{1}{3} \text{ } P(21|22) \text{ } \text{+} \text{ } \frac{2}{3} \text{ } P(31|22) \text{ } \text{-} \text{ } \frac{1}{3} \text{ } P(12|12) \text{ } \text{+} \text{ } \frac{2}{3} \text{ } P(22|12) \\ \text{-} \text{ } \frac{1}{3} \text{ } P(32|12) \text{ } \text{+} \text{ } \frac{1}{3} \text{ } P(12|22) \text{ } \text{+} \text{ } \frac{1}{3} \text{ } P(22|22) \text{ } \text{-} \text{ } \frac{2}{3} \text{ } P(32|22)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$
$$ \left (\begin{array}{c} \text{-} \text{ } 1 \text{ } P_(|) \text{ } \text{+} \text{ } 2 \text{ } P_A(1|2) \text{ } \text{+} \text{ } 2 \text{ } P_A(2|2) \text{ } \text{+} \text{ } 2 \text{ } P_AB(2,1|1,1) \\ \text{-} \text{ } 2 \text{ } P_AB(1,1|2,1) \text{ } \text{-} \text{ } 2 \text{ } P_AB(2,1|2,1) \text{ } \text{+} \text{ } 2 \text{ } P_B(1|2) \text{ } \text{-} \text{ } 2 \text{ } P_AB(2,1|1,2) \\ \text{-} \text{ } 2 \text{ } P_AB(1,1|2,2) \text{ } \text{-} \text{ } 2 \text{ } P_AB(2,1|2,2)\end{array}\right ) \le \left \{ \begin{array}{rl} \text{local:} & 1\text{ (facet)}\end{array} \right. $$

Symmetry group

Symmetry group of order: 8

Generators:

  • liftings :
    • A2(1,2)
    • A1(1,3)
  • outputInputPerms :
    • A1(2,3) A2(2,3) B2(1,2) A(1,2)

Extras